Overview of the Quantitative Histories Workshop

Nathan Alexander, Ph.D.

Author
Affiliations

Howard University

Assistant Professor

Department of Curriculum and Instruction | School of Education

MS Program | Center for Applied Data Science and Analytics

nathan.alexander@Howard.edu

Quantitative Histories Workshop

Curriculum & software development collective

and

research lab

Research Problem

Increasingly complex problems require complex tools.

Computational tools support interdisciplinary thinking.

Research Problem

Increasingly complex problems require complex tools.

Computational tools support interdisciplinary thinking.

Research Problem

Increasingly complex problems require complex tools.

Sub-disciplinary tools require interdisciplinary thinking.

How can information theory inform interdisciplinary curriculum and software development?

Information theory

Information theory is a branch of applied mathematics and computer science that deals with the quantification, storage, transmission, and manipulation of information. We take an abstract approach to our study of information.

  • Information theory seeks to measure the amount of information contained in a message or signal and how efficiently it can be transmitted or stored.

  • In this way, our projects define information using a curricular perspective.

Quantitative history

Historie Quantitative by Pierre Chaunu

Mathematical sociology

Journal of Mathematical Sociology

Curriculum and software development

Design, development, implementation, and evaluation of computational curricular materials

Research projects

  • ECHO: Education, Community, and Health Observations

    • Information and spatial segregation
  • Teaching statistical learning and mathematical modeling

  • Theory and quantification


Project group 1: Spatial information and racial isolation

How do patterns of racial segregation inform education, community, and health outcomes?

  • Historical legacies of injustice

  • Traditional modeling approaches

  • Modern computational tools

Dividing walls

Geometric approach

We adopt a topological model for spatial segregation on a geographical area, \(G\) to develop a theory of dividing walls.

Builds on the topological and topographical work of Short (2011).

Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.

Geographic area with neighborhood units

Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.

Geographic area with neighborhood units

Theorem 1. Given any configuration of blue and green towns, there is a dividing wall that separates blue towns from green towns.

Geographic area with wall dividing neighborhood units

Is there a dividing wall for an island with coastal towns?

Island with coastal towns

Is there a dividing wall for an island with coastal towns?

Minimal configuration

Alternating configuration (left) and non-alternating configuration (right).

Theorem 2. Alternating configurations of towns do not have a dividing wall, whereas non-alternating configurations of towns do have a dividing wall.


Algebraic approach

We then develop a algebraic modeling approach using methods from mathematical sociology.

Segregation indices

  • Dissimilarity index: Measures the proportion of one group’s population that would need to move to achieve an even distribution across all areas. It ranges from 0 to 1, with higher values indicating greater segregation.

  • Isolation index: Measures the extent to which members of a particular group are surrounded by others from the same group. It represents the percentage of people from a specific group who would need to change neighborhoods to achieve an even distribution. Higher values indicate higher isolation and segregation.


Algebraic approach

We then develop a algebraic modeling approach using methods from mathematical sociology.

Segregation indices

  • Exposure index: Measures the extent to which members of one group are exposed to members of another group. It quantifies the likelihood that a randomly selected individual from one group will encounter individuals from another group. Higher values indicate higher exposure and lower segregation.

  • Concentration index: Measures the extent to which a particular group is concentrated in specific areas or neighborhoods. It reflects the degree of clustering or dispersion of the group’s population across geographic units.

  • Gini index: Measure of income inequality, but it can also be adapted to measure residential segregation. It provides a summary measure of the overall distribution of different groups across neighborhoods.


Index of Dissimilarity

\[ D = \dfrac{1}{2} \sum_\limits{i=1}^n \bigg| \frac{b_i}{B} - \frac{w_i}{W} \bigg| \]

  • \(n\) is the number of neighborhoods in a geographic region,

  • \(b_i\) is the number of Black household units in neighborhood \(i\),

  • \(B\) is the total number of Black household units in the geographic region,

  • \(w_i\) is the number of non-Black household units in neighborhood \(i\),

  • \(W\) is the total number of non-Black household units in the geographic region,


Co-authored student research poster.

Computational approach

Teaching computational methods and open source tools makes for efficient and accurate learning. In about 20 lines of code, there is an immediate intersection.

black_georgetown_sc_2020 <-
  get_acs(geography = "tract", state = "SC",
          county = "Georgetown",
                        variable = "B02001_003", # Black or African American Alone
                        geometry = TRUE)
Getting data from the 2019-2023 5-year ACS
Downloading feature geometry from the Census website.  To cache shapefiles for use in future sessions, set `options(tigris_use_cache = TRUE)`.

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Estimate of Black or African American alone in Georgetown county, SC.

Getting data from the 2019-2023 5-year ACS
Downloading feature geometry from the Census website.  To cache shapefiles for use in future sessions, set `options(tigris_use_cache = TRUE)`.
Warning in title(...): "title" is not a graphical parameter
Warning in title(...): "subtitle" is not a graphical parameter
Warning in title(...): "title" is not a graphical parameter
Warning in title(...): "subtitle" is not a graphical parameter

Historical and broader applications

Social politics of maps.

  • Introductory module used in graduate course in statistics.

  • critstats package developed for students to download and explore culturally relevant data.


Historical applications

Distribution of Negroes in the United States.

Broader applications

True Size of Africa.

Project group 2: Mining archives and historical text: Analysis of sentiments and textual data

  • Inquiry into the speeches of historical figures, such as civil rights activists.

  • Exploration of journal articles and citations related to historical of inequity


Theoretical foundations of sentiment analysis

History, political science, and sociology inform theory development

Ida B. Wells-Barnett

W. E. B. Du Bois

Income and Expenditure of 150 Negroe Families in Atlanta

Hypothesis 1: Peaks in research occur within some key historical interval \((t_1, t_2)\).

Publications and citations related to racism in STEM education

Hypothesis 2: These intervals are lag models of broader system searches \((t_1, t_2)\).

Searches related to racism

Products

  • critstats software package. An abstract introduction to critical statistics.

  • Playbook for educators to support and improve data science education.

Broad Implications

  • K-12 teaching and learning

    • This also exposes students to a diversity of problems and methods to solve those problems.
  • Computationally-focused research and training in higher education

    • Provides an equitable pathway and entry into “high information, high density” conversations.
  • Industry and professional organizations